MODERN PHYSICS
4th Edition
ISBN: 9781119624974
Author: Krane
Publisher: WILEY
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Chapter 2, Problem 29P
(a)
To determine
To show that relativistic kinetic energy is conserved according to observer
(b)
To determine
To show that relativistic kinetic energy is conserved according to observer
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A ball is thrown with an initial speed v, at an angle 6, with the horizontal. The horizontal range of the ball is R, and the ball reaches a maximum height R/4. In terms of R and g, find the following.
(a) the time interval during which the ball is in motion
2R
(b) the ball's speed at the peak of its path
v=
Rg 2
√ sin 26, V 3
(c) the initial vertical component of its velocity
Rg
sin ei
sin 20
(d) its initial speed
Rg
√ sin 20
×
(e) the angle 6, expressed in terms of arctan of a fraction.
1
(f) Suppose the ball is thrown at the same initial speed found in (d) but at the angle appropriate for reaching the greatest height that it can. Find this height.
hmax
R2
(g) Suppose the ball is thrown at the same initial speed but at the angle for greatest possible range. Find this maximum horizontal range.
Xmax
R√3
2
An outfielder throws a baseball to his catcher in an attempt to throw out a runner at home plate. The ball bounces once before reaching the catcher. Assume the angle at which the bounced ball leaves the ground is the same as the angle at which the outfielder threw it as shown in the figure, but that the ball's speed after the bounce is one-half of what it was before the bounce.
8
(a) Assuming the ball is always thrown with the same initial speed, at what angle & should the fielder throw the ball to make it go the same distance D with one bounce (blue path) as a ball thrown upward at 35.0° with no bounce (green path)?
24
(b) Determine the ratio of the time interval for the one-bounce throw to the flight time for the no-bounce throw.
Cone-bounce
no-bounce
0.940
Chapter 2 Solutions
MODERN PHYSICS
Ch. 2 - Prob. 1QCh. 2 - Prob. 2QCh. 2 - Describe the situation of Figure 2.4 as it would...Ch. 2 - Does the Michelson–Morley experiment show that the...Ch. 2 - Suppose we made a pair of shears in which the...Ch. 2 - Light travels through water at a speed of about...Ch. 2 - Is it possible to have particles that travel at...Ch. 2 - How does relativity combine space and time...Ch. 2 - Einstein developed the relativity theory after...Ch. 2 - Explain in your own words the terms time dilation...
Ch. 2 - Does the Moon’s disk appear to be a different size...Ch. 2 - According to the time dilation effect, would the...Ch. 2 - Criticize the following argument. “Here is a way...Ch. 2 - Is it possible to synchronize clocks that are in...Ch. 2 - Suppose event A causes event B. To one observer,...Ch. 2 - Is mass a conserved quantity in classical physics?...Ch. 2 - “In special relativity, mass and energy are...Ch. 2 - Which is more massive, an object at low...Ch. 2 - Prob. 19QCh. 2 - Prob. 20QCh. 2 - You are piloting a small airplane in which you...Ch. 2 - A moving sidewalk 95 m in length carries...Ch. 2 - Prob. 3PCh. 2 - Prob. 4PCh. 2 - Prob. 5PCh. 2 - An astronaut must journey to a distant planet,...Ch. 2 - The proper lifetime of a certain particle is 120.0...Ch. 2 - High-energy particles are observed in laboratories...Ch. 2 - Prob. 9PCh. 2 - Two spaceships approach the Earth from opposite...Ch. 2 - Rocket A leaves a space station with a speed of...Ch. 2 - One of the strongest emission lines observed from...Ch. 2 - Prob. 13PCh. 2 - Three rods are joined to form a 45–45–90 triangle,...Ch. 2 - In the Relativistic Heavy Ion Collider (an...Ch. 2 - Derive the Lorentz velocity transformations for ...Ch. 2 - Observer O fires a light beam in the y direction...Ch. 2 - A light bulb at point x in the frame of reference...Ch. 2 - A neutral K meson at rest decays into two π...Ch. 2 - A rod in the reference frame of observer O makes...Ch. 2 - Two events occur at locations separated by a...Ch. 2 - According to observer O, a blue flash occurs at xb...Ch. 2 - Suppose the speed of light were 1000 mi/h. You are...Ch. 2 - Suppose rocket traveler Amelia has a clock made on...Ch. 2 - Suppose Amelia traveled at a speed of 0.80c to a...Ch. 2 - Make a drawing similar to Figure 2.20 showing the...Ch. 2 - Two twins make a round-trip journey from Earth to...Ch. 2 - Agnes makes a round trip at a constant speed to a...Ch. 2 - (a) Using the relativistically correct final...Ch. 2 - Find the momentum, kinetic energy, and total...Ch. 2 - An electron is moving with a kinetic energy of...Ch. 2 - Prob. 32PCh. 2 - Prob. 33PCh. 2 - Prob. 34PCh. 2 - Use Equations 2.32 and 2.36 to derive Equation...Ch. 2 - By carrying the binomial expansion one term...Ch. 2 - (a) According to observer O, a certain particle...Ch. 2 - An electron is moving at a speed of 0.85c. By how...Ch. 2 - Prob. 39PCh. 2 - Find the kinetic energy of an electron moving at a...Ch. 2 - An electron and a proton are each accelerated...Ch. 2 - Prob. 42PCh. 2 - A π meson of rest energy 139.6 MeV moving at a...Ch. 2 - An electron and a positron (an antielectron) make...Ch. 2 - It is desired to create a particle of mass 9460...Ch. 2 - A particle of rest energy mc2 is moving with speed...Ch. 2 - Let’s consider a different approach to Example...Ch. 2 - In the muon decay experiment discussed in Section...Ch. 2 - Derive the relativistic expression p2/2K = m +...Ch. 2 - Suppose we want to send an astronaut on a round...Ch. 2 - Prob. 52PCh. 2 - Observer O sees a red flash of light at the origin...Ch. 2 - Several spacecraft leave a space station at the...Ch. 2 - Observer O sees a light turn on at x = 524 m when...Ch. 2 - Suppose an observer O measures a particle of mass...Ch. 2 - Prob. 59PCh. 2 - A beam of 2.14 × 1011 electrons/s moving at a...Ch. 2 - An electron moving at a speed of vi = 0.960c in...Ch. 2 - A pion has a rest energy of 135 MeV. It decays...Ch. 2 - Prob. 63P
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